LMFDB - Embedded newform 700.2.c.i.699.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(699,700)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("700.699");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			699.2
Root			$-1.17915 - 0.780776i$ of defining polynomial
Character	$\chi$	$=$	700.699
Dual form			700.2.c.i.699.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17915 + 0.780776i) q^{2} -3.02045i q^{3} +(0.780776 - 1.84130i) q^{4} +(2.35829 + 3.56155i) q^{6} +(-1.51022 - 2.17238i) q^{7} +(0.516994 + 2.78078i) q^{8} -6.12311 q^{9} +O(q^{10})$	\(q+(-1.17915 + 0.780776i) q^{2} -3.02045i q^{3} +(0.780776 - 1.84130i) q^{4} +(2.35829 + 3.56155i) q^{6} +(-1.51022 - 2.17238i) q^{7} +(0.516994 + 2.78078i) q^{8} -6.12311 q^{9} +4.71659i q^{11} +(-5.56155 - 2.35829i) q^{12} -2.00000 q^{13} +(3.47692 + 1.38241i) q^{14} +(-2.78078 - 2.87529i) q^{16} +1.12311 q^{17} +(7.22004 - 4.78078i) q^{18} -4.71659 q^{19} +(-6.56155 + 4.56155i) q^{21} +(-3.68260 - 5.56155i) q^{22} -6.41273 q^{23} +(8.39919 - 1.56155i) q^{24} +(2.35829 - 1.56155i) q^{26} +9.43318i q^{27} +(-5.17915 + 1.08464i) q^{28} +2.00000 q^{29} +3.39228 q^{31} +(5.52390 + 1.21922i) q^{32} +14.2462 q^{33} +(-1.32431 + 0.876894i) q^{34} +(-4.78078 + 11.2745i) q^{36} -2.00000i q^{37} +(5.56155 - 3.68260i) q^{38} +6.04090i q^{39} -1.12311i q^{41} +(4.17548 - 10.5018i) q^{42} +0.371834 q^{43} +(8.68466 + 3.68260i) q^{44} +(7.56155 - 5.00691i) q^{46} +5.08842i q^{47} +(-8.68466 + 8.39919i) q^{48} +(-2.43845 + 6.56155i) q^{49} -3.39228i q^{51} +(-1.56155 + 3.68260i) q^{52} +2.00000i q^{53} +(-7.36520 - 11.1231i) q^{54} +(5.26012 - 5.32270i) q^{56} +14.2462i q^{57} +(-2.35829 + 1.56155i) q^{58} -2.06798 q^{59} +2.00000i q^{61} +(-4.00000 + 2.64861i) q^{62} +(9.24726 + 13.3017i) q^{63} +(-7.46543 + 2.87529i) q^{64} +(-16.7984 + 11.1231i) q^{66} -3.76412 q^{67} +(0.876894 - 2.06798i) q^{68} +19.3693i q^{69} -7.36520i q^{71} +(-3.16561 - 17.0270i) q^{72} -15.3693 q^{73} +(1.56155 + 2.35829i) q^{74} +(-3.68260 + 8.68466i) q^{76} +(10.2462 - 7.12311i) q^{77} +(-4.71659 - 7.12311i) q^{78} -1.32431i q^{79} +10.1231 q^{81} +(0.876894 + 1.32431i) q^{82} -3.02045i q^{83} +(3.27608 + 15.6433i) q^{84} +(-0.438447 + 0.290319i) q^{86} -6.04090i q^{87} +(-13.1158 + 2.43845i) q^{88} -12.0000i q^{89} +(3.02045 + 4.34475i) q^{91} +(-5.00691 + 11.8078i) q^{92} -10.2462i q^{93} +(-3.97292 - 6.00000i) q^{94} +(3.68260 - 16.6847i) q^{96} -1.12311 q^{97} +(-2.24782 - 9.64092i) q^{98} -28.8802i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 16 q^{9}+O(q^{10}) $ 8 * q - 2 * q^4 - 16 * q^9	$ 8 q - 2 q^{4} - 16 q^{9} - 28 q^{12} - 16 q^{13} + 6 q^{14} - 14 q^{16} - 24 q^{17} - 36 q^{21} - 32 q^{28} + 16 q^{29} + 48 q^{33} - 30 q^{36} + 28 q^{38} - 12 q^{42} + 20 q^{44} + 44 q^{46} - 20 q^{48} - 36 q^{49} + 4 q^{52} + 2 q^{56} - 32 q^{62} - 2 q^{64} + 40 q^{68} - 24 q^{73} - 4 q^{74} + 16 q^{77} + 48 q^{81} + 40 q^{82} - 8 q^{84} - 20 q^{86} + 24 q^{97} - 8 q^{98}+O(q^{100}) $ 8 * q - 2 * q^4 - 16 * q^9 - 28 * q^12 - 16 * q^13 + 6 * q^14 - 14 * q^16 - 24 * q^17 - 36 * q^21 - 32 * q^28 + 16 * q^29 + 48 * q^33 - 30 * q^36 + 28 * q^38 - 12 * q^42 + 20 * q^44 + 44 * q^46 - 20 * q^48 - 36 * q^49 + 4 * q^52 + 2 * q^56 - 32 * q^62 - 2 * q^64 + 40 * q^68 - 24 * q^73 - 4 * q^74 + 16 * q^77 + 48 * q^81 + 40 * q^82 - 8 * q^84 - 20 * q^86 + 24 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.17915	+	0.780776i	−0.833783	+	0.552092i
$2$	−1.17915	+	0.780776i	−0.833783	+	0.552092i
$3$		−	3.02045i		−	1.74386i	−0.489634	−	0.871928i	$-0.662870\pi$
$3$		−	3.02045i		−	1.74386i	0.489634	−	0.871928i	$-0.337130\pi$
$4$	0.780776	−	1.84130i	0.390388	−	0.920650i
$5$		0			0
$5$		0			0
$6$	2.35829	+	3.56155i	0.962770	+	1.45400i
$7$	−1.51022	−	2.17238i	−0.570811	−	0.821081i
$7$	−1.51022	−	2.17238i	−0.570811	−	0.821081i
$8$	0.516994	+	2.78078i	0.182785	+	0.983153i
$9$	−6.12311			−2.04104
$10$		0			0
$11$			4.71659i			1.42211i	0.703139	+	0.711053i	$0.251781\pi$
$11$			4.71659i			1.42211i	−0.703139	+	0.711053i	$0.748219\pi$
$12$	−5.56155	−	2.35829i	−1.60548	−	0.680781i
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$	3.47692	+	1.38241i	0.929245	+	0.369463i
$15$		0			0
$16$	−2.78078	−	2.87529i	−0.695194	−	0.718822i
$17$	1.12311			0.272393			0.136197	−	0.990682i	$-0.456512\pi$
$17$	1.12311			0.272393			0.136197	+	0.990682i	$0.456512\pi$
$18$	7.22004	−	4.78078i	1.70178	−	1.12684i
$19$	−4.71659			−1.08206			−0.541030	−	0.841003i	$-0.681965\pi$
$19$	−4.71659			−1.08206			−0.541030	+	0.841003i	$0.681965\pi$
$20$		0			0
$21$	−6.56155	+	4.56155i	−1.43185	+	0.995412i
$22$	−3.68260	−	5.56155i	−0.785133	−	1.18573i
$23$	−6.41273			−1.33715			−0.668573	−	0.743646i	$-0.733095\pi$
$23$	−6.41273			−1.33715			−0.668573	+	0.743646i	$0.733095\pi$
$24$	8.39919	−	1.56155i	1.71448	−	0.318751i
$25$		0			0
$26$	2.35829	−	1.56155i	0.462500	−	0.306246i
$27$			9.43318i			1.81542i
$28$	−5.17915	+	1.08464i	−0.978767	+	0.204977i
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$	3.39228			0.609272			0.304636	−	0.952469i	$-0.401465\pi$
$31$	3.39228			0.609272			0.304636	+	0.952469i	$0.401465\pi$
$32$	5.52390	+	1.21922i	0.976497	+	0.215530i
$33$	14.2462			2.47995
$34$	−1.32431	+	0.876894i	−0.227117	+	0.150386i
$35$		0			0
$36$	−4.78078	+	11.2745i	−0.796796	+	1.87908i
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$	5.56155	−	3.68260i	0.902203	−	0.597397i
$39$			6.04090i			0.967317i
$40$		0			0
$41$		−	1.12311i		−	0.175400i	−0.996147	−	0.0876998i	$-0.972048\pi$
$41$		−	1.12311i		−	0.175400i	0.996147	−	0.0876998i	$-0.0279516\pi$
$42$	4.17548	−	10.5018i	0.644291	−	1.62047i
$43$	0.371834			0.0567042			0.0283521	−	0.999598i	$-0.490974\pi$
$43$	0.371834			0.0567042			0.0283521	+	0.999598i	$0.490974\pi$
$44$	8.68466	+	3.68260i	1.30926	+	0.555173i
$45$		0			0
$46$	7.56155	−	5.00691i	1.11489	−	0.738228i
$47$			5.08842i			0.742223i	0.928588	+	0.371111i	$0.121023\pi$
$47$			5.08842i			0.742223i	−0.928588	+	0.371111i	$0.878977\pi$
$48$	−8.68466	+	8.39919i	−1.25352	+	1.21232i
$49$	−2.43845	+	6.56155i	−0.348350	+	0.937365i
$50$		0			0
$51$		−	3.39228i		−	0.475014i
$52$	−1.56155	+	3.68260i	−0.216548	+	0.510685i
$53$			2.00000i			0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$			2.00000i			0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$	−7.36520	−	11.1231i	−1.00228	−	1.51366i
$55$		0			0
$56$	5.26012	−	5.32270i	0.702913	−	0.711276i
$57$			14.2462i			1.88696i
$58$	−2.35829	+	1.56155i	−0.309659	+	0.205042i
$59$	−2.06798			−0.269227			−0.134614	−	0.990898i	$-0.542979\pi$
$59$	−2.06798			−0.269227			−0.134614	+	0.990898i	$0.542979\pi$
$60$		0			0
$61$			2.00000i			0.256074i	0.991769	+	0.128037i	$0.0408676\pi$
$61$			2.00000i			0.256074i	−0.991769	+	0.128037i	$0.959132\pi$
$62$	−4.00000	+	2.64861i	−0.508001	+	0.336374i
$63$	9.24726	+	13.3017i	1.16505	+	1.67586i
$64$	−7.46543	+	2.87529i	−0.933179	+	0.359411i
$65$		0			0
$66$	−16.7984	+	11.1231i	−2.06774	+	1.36916i
$67$	−3.76412			−0.459860			−0.229930	−	0.973207i	$-0.573850\pi$
$67$	−3.76412			−0.459860			−0.229930	+	0.973207i	$0.573850\pi$
$68$	0.876894	−	2.06798i	0.106339	−	0.250779i
$69$			19.3693i			2.33179i
$70$		0			0
$71$		−	7.36520i		−	0.874089i	−0.899440	−	0.437044i	$-0.856025\pi$
$71$		−	7.36520i		−	0.874089i	0.899440	−	0.437044i	$-0.143975\pi$
$72$	−3.16561	−	17.0270i	−0.373070	−	2.00665i
$73$	−15.3693			−1.79884			−0.899421	−	0.437083i	$-0.856012\pi$
$73$	−15.3693			−1.79884			−0.899421	+	0.437083i	$0.856012\pi$
$74$	1.56155	+	2.35829i	0.181527	+	0.274146i
$75$		0			0
$76$	−3.68260	+	8.68466i	−0.422423	+	0.996199i
$77$	10.2462	−	7.12311i	1.16766	−	0.811753i
$78$	−4.71659	−	7.12311i	−0.534049	−	0.806533i
$79$		−	1.32431i		−	0.148996i	−0.997221	−	0.0744981i	$-0.976265\pi$
$79$		−	1.32431i		−	0.148996i	0.997221	−	0.0744981i	$-0.0237355\pi$
$80$		0			0
$81$	10.1231			1.12479
$82$	0.876894	+	1.32431i	0.0968368	+	0.146245i
$83$		−	3.02045i		−	0.331537i	−0.986165	−	0.165769i	$-0.946990\pi$
$83$		−	3.02045i		−	0.331537i	0.986165	−	0.165769i	$-0.0530105\pi$
$84$	3.27608	+	15.6433i	0.357450	+	1.70683i
$85$		0			0
$86$	−0.438447	+	0.290319i	−0.0472790	+	0.0313059i
$87$		−	6.04090i		−	0.647652i
$88$	−13.1158	+	2.43845i	−1.39815	+	0.259939i
$89$		−	12.0000i		−	1.27200i	−0.771690	−	0.635999i	$-0.780588\pi$
$89$		−	12.0000i		−	1.27200i	0.771690	−	0.635999i	$-0.219412\pi$
$90$		0			0
$91$	3.02045	+	4.34475i	0.316629	+	0.455454i
$92$	−5.00691	+	11.8078i	−0.522006	+	1.23104i
$93$		−	10.2462i		−	1.06248i
$94$	−3.97292	−	6.00000i	−0.409775	−	0.618853i
$95$		0			0
$96$	3.68260	−	16.6847i	0.375854	−	1.70287i
$97$	−1.12311			−0.114034			−0.0570170	−	0.998373i	$-0.518159\pi$
$97$	−1.12311			−0.114034			−0.0570170	+	0.998373i	$0.518159\pi$
$98$	−2.24782	−	9.64092i	−0.227064	−	0.973880i
$99$		−	28.8802i		−	2.90257i
$100$		0			0
$101$		−	15.1231i		−	1.50481i	−0.658703	−	0.752403i	$-0.728895\pi$
$101$		−	15.1231i		−	1.50481i	0.658703	−	0.752403i	$-0.271105\pi$
$102$	2.64861	+	4.00000i	0.262252	+	0.396059i
$103$			7.73704i			0.762353i	0.924502	+	0.381176i	$0.124481\pi$
$103$			7.73704i			0.762353i	−0.924502	+	0.381176i	$0.875519\pi$
$104$	−1.03399	−	5.56155i	−0.101391	−	0.545355i
$105$		0			0
$106$	−1.56155	−	2.35829i	−0.151671	−	0.229058i
$107$	−5.66906			−0.548049			−0.274024	−	0.961723i	$-0.588355\pi$
$107$	−5.66906			−0.548049			−0.274024	+	0.961723i	$0.588355\pi$
$108$	17.3693	+	7.36520i	1.67136	+	0.708717i
$109$	7.12311			0.682270			0.341135	−	0.940014i	$-0.389189\pi$
$109$	7.12311			0.682270			0.341135	+	0.940014i	$0.389189\pi$
$110$		0			0
$111$	−6.04090			−0.573376
$112$	−2.04662	+	10.3832i	−0.193387	+	0.981123i
$113$			18.4924i			1.73962i	0.493386	+	0.869810i	$0.335759\pi$
$113$			18.4924i			1.73962i	−0.493386	+	0.869810i	$0.664241\pi$
$114$	−11.1231	−	16.7984i	−1.04177	−	1.57331i
$115$		0			0
$116$	1.56155	−	3.68260i	0.144987	−	0.341921i
$117$	12.2462			1.13216
$118$	2.43845	−	1.61463i	0.224477	−	0.148638i
$119$	−1.69614	−	2.43981i	−0.155485	−	0.223657i
$120$		0			0
$121$	−11.2462			−1.02238
$122$	−1.56155	−	2.35829i	−0.141376	−	0.213510i
$123$	−3.39228			−0.305872
$124$	2.64861	−	6.24621i	0.237853	−	0.560926i
$125$		0			0
$126$	−21.2895	−	8.46462i	−1.89662	−	0.754088i
$127$	−17.7509			−1.57513			−0.787567	−	0.616229i	$-0.788659\pi$
$127$	−17.7509			−1.57513			−0.787567	+	0.616229i	$0.788659\pi$
$128$	6.55789	−	9.21922i	0.579641	−	0.814872i
$129$		−	1.12311i		−	0.0988839i
$130$		0			0
$131$	−17.5420			−1.53266			−0.766328	−	0.642450i	$-0.777918\pi$
$131$	−17.5420			−1.53266			−0.766328	+	0.642450i	$0.777918\pi$
$132$	11.1231	−	26.2316i	0.968142	−	2.28316i
$133$	7.12311	+	10.2462i	0.617652	+	0.888459i
$134$	4.43845	−	2.93893i	0.383423	−	0.253885i
$135$		0			0
$136$	0.580639	+	3.12311i	0.0497894	+	0.267804i
$137$			14.0000i			1.19610i	0.801459	+	0.598050i	$0.204058\pi$
$137$			14.0000i			1.19610i	−0.801459	+	0.598050i	$0.795942\pi$
$138$	−15.1231	−	22.8393i	−1.28736	−	1.94421i
$139$	16.7984			1.42482			0.712410	−	0.701763i	$-0.247604\pi$
$139$	16.7984			1.42482			0.712410	+	0.701763i	$0.247604\pi$
$140$		0			0
$141$	15.3693			1.29433
$142$	5.75058	+	8.68466i	0.482578	+	0.728800i
$143$		−	9.43318i		−	0.788842i
$144$	17.0270	+	17.6057i	1.41892	+	1.46714i
$145$		0			0
$146$	18.1227	−	12.0000i	1.49984	−	0.993127i
$147$	19.8188	+	7.36520i	1.63463	+	0.607472i
$148$	−3.68260	−	1.56155i	−0.302708	−	0.128359i
$149$	−5.36932			−0.439872			−0.219936	−	0.975514i	$-0.570585\pi$
$149$	−5.36932			−0.439872			−0.219936	+	0.975514i	$0.570585\pi$
$150$		0			0
$151$		−	10.0138i		−	0.814913i	−0.913225	−	0.407456i	$-0.866416\pi$
$151$		−	10.0138i		−	0.814913i	0.913225	−	0.407456i	$-0.133584\pi$
$152$	−2.43845	−	13.1158i	−0.197784	−	1.06383i
$153$	−6.87689			−0.555964
$154$	−6.52024	+	16.3992i	−0.525416	+	1.32148i
$155$		0			0
$156$	11.1231	+	4.71659i	0.890561	+	0.377629i
$157$	−0.246211			−0.0196498			−0.00982490	−	0.999952i	$-0.503127\pi$
$157$	−0.246211			−0.0196498			−0.00982490	+	0.999952i	$0.503127\pi$
$158$	1.03399	+	1.56155i	0.0822596	+	0.124230i
$159$	6.04090			0.479074
$160$		0			0
$161$	9.68466	+	13.9309i	0.763258	+	1.09791i
$162$	−11.9366	+	7.90388i	−0.937830	+	0.620988i
$163$	−3.02045			−0.236580			−0.118290	−	0.992979i	$-0.537741\pi$
$163$	−3.02045			−0.236580			−0.118290	+	0.992979i	$0.537741\pi$
$164$	−2.06798	−	0.876894i	−0.161482	−	0.0684739i
$165$		0			0
$166$	2.35829	+	3.56155i	0.183039	+	0.276430i
$167$		−	19.8188i		−	1.53363i	−0.641870	−	0.766813i	$-0.721841\pi$
$167$		−	19.8188i		−	1.53363i	0.641870	−	0.766813i	$-0.278159\pi$
$168$	−16.0769	−	15.8879i	−1.24036	−	1.22578i
$169$	−9.00000			−0.692308
$170$		0			0
$171$	28.8802			2.20852
$172$	0.290319	−	0.684658i	0.0221366	−	0.0522047i
$173$	16.2462			1.23518			0.617588	−	0.786502i	$-0.288110\pi$
$173$	16.2462			1.23518			0.617588	+	0.786502i	$0.288110\pi$
$174$	4.71659	+	7.12311i	0.357564	+	0.540001i
$175$		0			0
$176$	13.5616	−	13.1158i	1.02224	−	0.988639i
$177$			6.24621i			0.469494i
$178$	9.36932	+	14.1498i	0.702260	+	1.06057i
$179$			10.7575i			0.804052i	0.915628	+	0.402026i	$0.131694\pi$
$179$			10.7575i			0.804052i	−0.915628	+	0.402026i	$0.868306\pi$
$180$		0			0
$181$		−	15.1231i		−	1.12409i	−0.827106	−	0.562046i	$-0.810014\pi$
$181$		−	15.1231i		−	1.12409i	0.827106	−	0.562046i	$-0.189986\pi$
$182$	−6.95383	−	2.76481i	−0.515453	−	0.204941i
$183$	6.04090			0.446556
$184$	−3.31534	−	17.8324i	−0.244410	−	1.31462i
$185$		0			0
$186$	8.00000	+	12.0818i	0.586588	+	0.885880i
$187$			5.29723i			0.387372i
$188$	9.36932	+	3.97292i	0.683328	+	0.289755i
$189$	20.4924	−	14.2462i	1.49060	−	1.03626i
$190$		0			0
$191$			16.7984i			1.21549i	0.794133	+	0.607744i	$0.207925\pi$
$191$			16.7984i			1.21549i	−0.794133	+	0.607744i	$0.792075\pi$
$192$	8.68466	+	22.5490i	0.626761	+	1.62733i
$193$		−	22.4924i		−	1.61904i	−0.587092	−	0.809520i	$-0.699727\pi$
$193$		−	22.4924i		−	1.61904i	0.587092	−	0.809520i	$-0.300273\pi$
$194$	1.32431	−	0.876894i	0.0950797	−	0.0629573i
$195$		0			0
$196$	10.1779	+	9.61302i	0.726994	+	0.686644i
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$	22.5490	+	34.0540i	1.60248	+	2.42011i
$199$	−26.8122			−1.90067			−0.950333	−	0.311235i	$-0.899258\pi$
$199$	−26.8122			−1.90067			−0.950333	+	0.311235i	$0.899258\pi$
$200$		0			0
$201$			11.3693i			0.801930i
$202$	11.8078	+	17.8324i	0.830791	+	1.25468i
$203$	−3.02045	−	4.34475i	−0.211994	−	0.304942i
$204$	−6.24621	−	2.64861i	−0.437322	−	0.185440i
$205$		0			0
$206$	−6.04090	−	9.12311i	−0.420889	−	0.635637i
$207$	39.2658			2.72916
$208$	5.56155	+	5.75058i	0.385624	+	0.398731i
$209$		−	22.2462i		−	1.53880i
$210$		0			0
$211$			22.0956i			1.52112i	0.649265	+	0.760562i	$0.275077\pi$
$211$			22.0956i			1.52112i	−0.649265	+	0.760562i	$0.724923\pi$
$212$	3.68260	+	1.56155i	0.252922	+	0.107248i
$213$	−22.2462			−1.52429
$214$	6.68466	−	4.42627i	0.456954	−	0.302574i
$215$		0			0
$216$	−26.2316	+	4.87689i	−1.78483	+	0.331831i
$217$	−5.12311	−	7.36932i	−0.347779	−	0.500262i
$218$	−8.39919	+	5.56155i	−0.568865	+	0.376676i
$219$			46.4222i			3.13692i
$220$		0			0
$221$	−2.24621			−0.151097
$222$	7.12311	−	4.71659i	0.478072	−	0.316557i
$223$		−	20.5625i		−	1.37697i	−0.725252	−	0.688483i	$-0.758277\pi$
$223$		−	20.5625i		−	1.37697i	0.725252	−	0.688483i	$-0.241723\pi$
$224$	−5.69372	−	13.8413i	−0.380427	−	0.924811i
$225$		0			0
$226$	−14.4384	−	21.8053i	−0.960431	−	1.45047i
$227$		−	3.76412i		−	0.249833i	−0.992167	−	0.124917i	$-0.960134\pi$
$227$		−	3.76412i		−	0.249833i	0.992167	−	0.124917i	$-0.0398663\pi$
$228$	26.2316	+	11.1231i	1.73723	+	0.736646i
$229$			12.8769i			0.850929i	0.904975	+	0.425465i	$0.139889\pi$
$229$			12.8769i			0.850929i	−0.904975	+	0.425465i	$0.860111\pi$
$230$		0			0
$231$	−21.5150	−	30.9481i	−1.41558	−	2.03624i
$232$	1.03399	+	5.56155i	0.0678846	+	0.365134i
$233$			7.75379i			0.507968i	0.967208	+	0.253984i	$0.0817410\pi$
$233$			7.75379i			0.507968i	−0.967208	+	0.253984i	$0.918259\pi$
$234$	−14.4401	+	9.56155i	−0.943978	+	0.625058i
$235$		0			0
$236$	−1.61463	+	3.80776i	−0.105103	+	0.247864i
$237$	−4.00000			−0.259828
$238$	3.90495	+	1.55259i	0.253120	+	0.100639i
$239$		−	3.97292i		−	0.256987i	−0.991710	−	0.128493i	$-0.958986\pi$
$239$		−	3.97292i		−	0.256987i	0.991710	−	0.128493i	$-0.0410141\pi$
$240$		0			0
$241$		−	25.6155i		−	1.65004i	−0.565103	−	0.825021i	$-0.691163\pi$
$241$		−	25.6155i		−	1.65004i	0.565103	−	0.825021i	$-0.308837\pi$
$242$	13.2609	−	8.78078i	0.852445	−	0.564450i
$243$		−	2.27678i		−	0.146055i
$244$	3.68260	+	1.56155i	0.235754	+	0.0999682i
$245$		0			0
$246$	4.00000	−	2.64861i	0.255031	−	0.168869i
$247$	9.43318			0.600219
$248$	1.75379	+	9.43318i	0.111366	+	0.599007i
$249$	−9.12311			−0.578153
$250$		0			0
$251$	16.0547			1.01336			0.506682	−	0.862133i	$-0.330872\pi$
$251$	16.0547			1.01336			0.506682	+	0.862133i	$0.330872\pi$
$252$	31.7125	−	6.64134i	1.99770	−	0.418365i
$253$		−	30.2462i		−	1.90156i
$254$	20.9309	−	13.8594i	1.31332	−	0.869619i
$255$		0			0
$256$	−0.534565	+	15.9911i	−0.0334103	+	0.999442i
$257$	−11.3693			−0.709199			−0.354599	−	0.935018i	$-0.615383\pi$
$257$	−11.3693			−0.709199			−0.354599	+	0.935018i	$0.615383\pi$
$258$	0.876894	+	1.32431i	0.0545931	+	0.0824477i
$259$	−4.34475	+	3.02045i	−0.269970	+	0.187682i
$260$		0			0
$261$	−12.2462			−0.758021
$262$	20.6847	−	13.6964i	1.27790	−	0.846168i
$263$	18.4945			1.14042			0.570211	−	0.821499i	$-0.306862\pi$
$263$	18.4945			1.14042			0.570211	+	0.821499i	$0.306862\pi$
$264$	7.36520	+	39.6155i	0.453297	+	2.43817i
$265$		0			0
$266$	−16.3992	−	6.52024i	−1.00550	−	0.399781i
$267$	−36.2454			−2.21818
$268$	−2.93893	+	6.93087i	−0.179524	+	0.423370i
$269$			0.246211i			0.0150118i	0.999972	+	0.00750588i	$0.00238922\pi$
$269$			0.246211i			0.0150118i	−0.999972	+	0.00750588i	$0.997611\pi$
$270$		0			0
$271$	−1.90495			−0.115717			−0.0578586	−	0.998325i	$-0.518427\pi$
$271$	−1.90495			−0.115717			−0.0578586	+	0.998325i	$0.518427\pi$
$272$	−3.12311	−	3.22925i	−0.189366	−	0.195802i
$273$	13.1231	−	9.12311i	0.794246	−	0.552155i
$274$	−10.9309	−	16.5081i	−0.660358	−	0.997288i
$275$		0			0
$276$	35.6647	+	15.1231i	2.14676	+	0.910304i
$277$		−	12.2462i		−	0.735804i	−0.929865	−	0.367902i	$-0.880076\pi$
$277$		−	12.2462i		−	0.735804i	0.929865	−	0.367902i	$-0.119924\pi$
$278$	−19.8078	+	13.1158i	−1.18799	+	0.786632i
$279$	−20.7713			−1.24355
$280$		0			0
$281$	−29.3693			−1.75203			−0.876013	−	0.482287i	$-0.839806\pi$
$281$	−29.3693			−1.75203			−0.876013	+	0.482287i	$0.839806\pi$
$282$	−18.1227	+	12.0000i	−1.07919	+	0.714590i
$283$			4.92539i			0.292784i	0.989227	+	0.146392i	$0.0467661\pi$
$283$			4.92539i			0.292784i	−0.989227	+	0.146392i	$0.953234\pi$
$284$	−13.5616	−	5.75058i	−0.804730	−	0.341234i
$285$		0			0
$286$	7.36520	+	11.1231i	0.435514	+	0.657723i
$287$	−2.43981	+	1.69614i	−0.144017	+	0.100120i
$288$	−33.8234	−	7.46543i	−1.99307	−	0.439905i
$289$	−15.7386			−0.925802
$290$		0			0
$291$			3.39228i			0.198859i
$292$	−12.0000	+	28.2995i	−0.702247	+	1.65610i
$293$	15.7538			0.920346			0.460173	−	0.887829i	$-0.347787\pi$
$293$	15.7538			0.920346			0.460173	+	0.887829i	$0.347787\pi$
$294$	−29.1199	+	6.78942i	−1.69831	+	0.395967i
$295$		0			0
$296$	5.56155	−	1.03399i	0.323259	−	0.0600993i
$297$	−44.4924			−2.58171
$298$	6.33122	−	4.19224i	0.366757	−	0.242850i
$299$	12.8255			0.741715
$300$		0			0
$301$	−0.561553	−	0.807764i	−0.0323674	−	0.0465587i
$302$	7.81855	+	11.8078i	0.449907	+	0.679460i
$303$	−45.6786			−2.62416
$304$	13.1158	+	13.5616i	0.752242	+	0.777808i
$305$		0			0
$306$	8.10887	−	5.36932i	0.463553	−	0.306943i
$307$			1.53311i			0.0874993i	0.999043	+	0.0437496i	$0.0139304\pi$
$307$			1.53311i			0.0874993i	−0.999043	+	0.0437496i	$0.986070\pi$
$308$	−5.11578	−	24.4279i	−0.291499	−	1.39191i
$309$	23.3693			1.32943
$310$		0			0
$311$	−30.2045			−1.71274			−0.856369	−	0.516364i	$-0.827285\pi$
$311$	−30.2045			−1.71274			−0.856369	+	0.516364i	$0.827285\pi$
$312$	−16.7984	+	3.12311i	−0.951021	+	0.176811i
$313$	−33.6155			−1.90006			−0.950031	−	0.312156i	$-0.898949\pi$
$313$	−33.6155			−1.90006			−0.950031	+	0.312156i	$0.898949\pi$
$314$	0.290319	−	0.192236i	0.0163837	−	0.0108485i
$315$		0			0
$316$	−2.43845	−	1.03399i	−0.137173	−	0.0581663i
$317$		−	12.2462i		−	0.687816i	−0.939003	−	0.343908i	$-0.888249\pi$
$317$		−	12.2462i		−	0.687816i	0.939003	−	0.343908i	$-0.111751\pi$
$318$	−7.12311	+	4.71659i	−0.399444	+	0.264493i
$319$			9.43318i			0.528157i
$320$		0			0
$321$			17.1231i			0.955719i
$322$	−22.2965	−	8.86499i	−1.24254	−	0.494027i
$323$	−5.29723			−0.294746
$324$	7.90388	−	18.6397i	0.439105	−	1.03554i
$325$		0			0
$326$	3.56155	−	2.35829i	0.197256	−	0.130614i
$327$		−	21.5150i		−	1.18978i
$328$	3.12311	−	0.580639i	0.172445	−	0.0320604i
$329$	11.0540	−	7.68466i	0.609425	−	0.423669i
$330$		0			0
$331$			18.2857i			1.00507i	0.864556	+	0.502537i	$0.167600\pi$
$331$			18.2857i			1.00507i	−0.864556	+	0.502537i	$0.832400\pi$
$332$	−5.56155	−	2.35829i	−0.305230	−	0.129428i
$333$			12.2462i			0.671088i
$334$	15.4741	+	23.3693i	0.846704	+	1.27871i
$335$		0			0
$336$	31.3620	+	6.18170i	1.71094	+	0.337239i
$337$			12.2462i			0.667094i	0.942734	+	0.333547i	$0.108246\pi$
$337$			12.2462i			0.667094i	−0.942734	+	0.333547i	$0.891754\pi$
$338$	10.6123	−	7.02699i	0.577234	−	0.382218i
$339$	55.8554			3.03365
$340$		0			0
$341$			16.0000i			0.866449i
$342$	−34.0540	+	22.5490i	−1.84143	+	1.21931i
$343$	17.9368	−	4.61219i	0.968495	−	0.249035i
$344$	0.192236	+	1.03399i	0.0103647	+	0.0557489i
$345$		0			0
$346$	−19.1567	+	12.6847i	−1.02987	+	0.681931i
$347$	−5.66906			−0.304331			−0.152166	−	0.988355i	$-0.548625\pi$
$347$	−5.66906			−0.304331			−0.152166	+	0.988355i	$0.548625\pi$
$348$	−11.1231	−	4.71659i	−0.596261	−	0.252836i
$349$		−	29.8617i		−	1.59846i	−0.601024	−	0.799231i	$-0.705240\pi$
$349$		−	29.8617i		−	1.59846i	0.601024	−	0.799231i	$-0.294760\pi$
$350$		0			0
$351$		−	18.8664i		−	1.00701i
$352$	−5.75058	+	26.0540i	−0.306507	+	1.38868i
$353$	19.3693			1.03092			0.515462	−	0.856912i	$-0.327620\pi$
$353$	19.3693			1.03092			0.515462	+	0.856912i	$0.327620\pi$
$354$	−4.87689	−	7.36520i	−0.259204	−	0.391456i
$355$		0			0
$356$	−22.0956	−	9.36932i	−1.17106	−	0.496573i
$357$	−7.36932	+	5.12311i	−0.390026	+	0.271144i
$358$	−8.39919	−	12.6847i	−0.443911	−	0.670405i
$359$		−	16.0547i		−	0.847335i	−0.905818	−	0.423668i	$-0.860742\pi$
$359$		−	16.0547i		−	0.847335i	0.905818	−	0.423668i	$-0.139258\pi$
$360$		0			0
$361$	3.24621			0.170853
$362$	11.8078	+	17.8324i	0.620602	+	0.937248i
$363$			33.9686i			1.78289i
$364$	10.3583	−	2.16927i	0.542922	−	0.113701i
$365$		0			0
$366$	−7.12311	+	4.71659i	−0.372331	+	0.246540i
$367$		−	10.3857i		−	0.542127i	−0.962562	−	0.271063i	$-0.912625\pi$
$367$		−	10.3857i		−	0.542127i	0.962562	−	0.271063i	$-0.0873753\pi$
$368$	17.8324	+	18.4384i	0.929576	+	0.961171i
$369$			6.87689i			0.357997i
$370$		0			0
$371$	4.34475	−	3.02045i	0.225568	−	0.156814i
$372$	−18.8664	−	8.00000i	−0.978175	−	0.414781i
$373$		−	10.4924i		−	0.543277i	−0.962399	−	0.271639i	$-0.912434\pi$
$373$		−	10.4924i		−	0.543277i	0.962399	−	0.271639i	$-0.0875655\pi$
$374$	−4.13595	−	6.24621i	−0.213865	−	0.322984i
$375$		0			0
$376$	−14.1498	+	2.63068i	−0.729719	+	0.135667i
$377$	−4.00000			−0.206010
$378$	−13.0405	+	32.7984i	−0.670730	+	1.68697i
$379$		−	14.8934i		−	0.765024i	−0.923950	−	0.382512i	$-0.875059\pi$
$379$		−	14.8934i		−	0.765024i	0.923950	−	0.382512i	$-0.124941\pi$
$380$		0			0
$381$			53.6155i			2.74681i
$382$	−13.1158	−	19.8078i	−0.671062	−	1.01345i
$383$			19.0752i			0.974695i	0.873208	+	0.487348i	$0.162036\pi$
$383$			19.0752i			0.974695i	−0.873208	+	0.487348i	$0.837964\pi$
$384$	−27.8462	−	19.8078i	−1.42102	−	1.01081i
$385$		0			0
$386$	17.5616	+	26.5219i	0.893860	+	1.34993i
$387$	−2.27678			−0.115735
$388$	−0.876894	+	2.06798i	−0.0445176	+	0.104986i
$389$	7.12311			0.361156			0.180578	−	0.983561i	$-0.442203\pi$
$389$	7.12311			0.361156			0.180578	+	0.983561i	$0.442203\pi$
$390$		0			0
$391$	−7.20217			−0.364230
$392$	−19.5069	−	3.38849i	−0.985246	−	0.171145i
$393$			52.9848i			2.67273i
$394$	14.0540	+	21.2247i	0.708029	+	1.06928i
$395$		0			0
$396$	−53.1771	−	22.5490i	−2.67225	−	1.13313i
$397$	−14.0000			−0.702640			−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000			−0.702640			−0.351320	+	0.936255i	$0.614267\pi$
$398$	31.6155	−	20.9343i	1.58474	−	1.04934i
$399$	30.9481	−	21.5150i	1.54935	−	1.07710i
$400$		0			0
$401$	6.00000			0.299626			0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000			0.299626			0.149813	+	0.988714i	$0.452133\pi$
$402$	−8.87689	−	13.4061i	−0.442739	−	0.668635i
$403$	−6.78456			−0.337963
$404$	−27.8462	−	11.8078i	−1.38540	−	0.587458i
$405$		0			0
$406$	6.95383	+	2.76481i	0.345113	+	0.137215i
$407$	9.43318			0.467585
$408$	9.43318	−	1.75379i	0.467012	−	0.0868255i
$409$			17.1231i			0.846683i	0.905970	+	0.423342i	$0.139143\pi$
$409$			17.1231i			0.846683i	−0.905970	+	0.423342i	$0.860857\pi$
$410$		0			0
$411$	42.2863			2.08583
$412$	14.2462	+	6.04090i	0.701860	+	0.297614i
$413$	3.12311	+	4.49242i	0.153678	+	0.221058i
$414$	−46.3002	+	30.6578i	−2.27553	+	1.50675i
$415$		0			0
$416$	−11.0478	−	2.43845i	−0.541663	−	0.119555i
$417$		−	50.7386i		−	2.48468i
$418$	17.3693	+	26.2316i	0.849561	+	1.28303i
$419$	−23.5829			−1.15210			−0.576051	−	0.817414i	$-0.695407\pi$
$419$	−23.5829			−1.15210			−0.576051	+	0.817414i	$0.695407\pi$
$420$		0			0
$421$	23.6155			1.15095			0.575475	−	0.817819i	$-0.304817\pi$
$421$	23.6155			1.15095			0.575475	+	0.817819i	$0.304817\pi$
$422$	−17.2517	−	26.0540i	−0.839801	−	1.26829i
$423$		−	31.1570i		−	1.51490i
$424$	−5.56155	+	1.03399i	−0.270093	+	0.0502149i
$425$		0			0
$426$	26.2316	−	17.3693i	1.27092	−	0.841546i
$427$	4.34475	−	3.02045i	0.210257	−	0.146170i
$428$	−4.42627	+	10.4384i	−0.213952	+	0.504561i
$429$	−28.4924			−1.37563
$430$		0			0
$431$			5.87787i			0.283127i	0.989929	+	0.141563i	$0.0452129\pi$
$431$			5.87787i			0.283127i	−0.989929	+	0.141563i	$0.954787\pi$
$432$	27.1231	−	26.2316i	1.30496	−	1.26207i
$433$	−29.6155			−1.42323			−0.711616	−	0.702569i	$-0.752036\pi$
$433$	−29.6155			−1.42323			−0.711616	+	0.702569i	$0.752036\pi$
$434$	11.7947	+	4.68951i	0.566163	+	0.225104i
$435$		0			0
$436$	5.56155	−	13.1158i	0.266350	−	0.628132i
$437$	30.2462			1.44687
$438$	−36.2454	−	54.7386i	−1.73187	−	2.61551i
$439$	16.2177			0.774031			0.387015	−	0.922073i	$-0.373506\pi$
$439$	16.2177			0.774031			0.387015	+	0.922073i	$0.373506\pi$
$440$		0			0
$441$	14.9309	−	40.1771i	0.710994	−	1.91319i
$442$	2.64861	−	1.75379i	0.125982	−	0.0834192i
$443$	23.0481			1.09505			0.547524	−	0.836790i	$-0.315571\pi$
$443$	23.0481			1.09505			0.547524	+	0.836790i	$0.315571\pi$
$444$	−4.71659	+	11.1231i	−0.223839	+	0.527879i
$445$		0			0
$446$	16.0547	+	24.2462i	0.760213	+	1.14809i
$447$			16.2177i			0.767073i
$448$	17.5207	+	11.8754i	0.827775	+	0.561061i
$449$	15.6155			0.736942			0.368471	−	0.929639i	$-0.379881\pi$
$449$	15.6155			0.736942			0.368471	+	0.929639i	$0.379881\pi$
$450$		0			0
$451$	5.29723			0.249437
$452$	34.0501	+	14.4384i	1.60158	+	0.679127i
$453$	−30.2462			−1.42109
$454$	2.93893	+	4.43845i	0.137931	+	0.208307i
$455$		0			0
$456$	−39.6155	+	7.36520i	−1.85517	+	0.344907i
$457$		−	6.00000i		−	0.280668i	−0.990104	−	0.140334i	$-0.955182\pi$
$457$		−	6.00000i		−	0.280668i	0.990104	−	0.140334i	$-0.0448177\pi$
$458$	−10.0540	−	15.1838i	−0.469791	−	0.709490i
$459$			10.5945i			0.494507i
$460$		0			0
$461$			3.61553i			0.168392i	0.996449	+	0.0841960i	$0.0268322\pi$
$461$			3.61553i			0.168392i	−0.996449	+	0.0841960i	$0.973168\pi$
$462$	49.5329	+	19.6940i	2.30448	+	0.916250i
$463$	28.6714			1.33247			0.666236	−	0.745741i	$-0.267904\pi$
$463$	28.6714			1.33247			0.666236	+	0.745741i	$0.267904\pi$
$464$	−5.56155	−	5.75058i	−0.258189	−	0.266964i
$465$		0			0
$466$	−6.05398	−	9.14286i	−0.280445	−	0.423535i
$467$			18.4945i			0.855824i	0.903820	+	0.427912i	$0.140751\pi$
$467$			18.4945i			0.855824i	−0.903820	+	0.427912i	$0.859249\pi$
$468$	9.56155	−	22.5490i	0.441983	−	1.04233i
$469$	5.68466	+	8.17708i	0.262493	+	0.377583i
$470$		0			0
$471$			0.743668i			0.0342664i
$472$	−1.06913	−	5.75058i	−0.0492107	−	0.264692i
$473$			1.75379i			0.0806393i
$474$	4.71659	−	3.12311i	0.216640	−	0.143449i
$475$		0			0
$476$	−5.81673	+	1.21816i	−0.266609	+	0.0558343i
$477$		−	12.2462i		−	0.560715i
$478$	3.10196	+	4.68466i	0.141880	+	0.214271i
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$			4.00000i			0.182384i
$482$	20.0000	+	30.2045i	0.910975	+	1.37578i
$483$	42.0775	−	29.2520i	1.91459	−	1.33101i
$484$	−8.78078	+	20.7077i	−0.399126	+	0.941257i
$485$		0			0
$486$	1.77766	+	2.68466i	0.0806361	+	0.121779i
$487$	13.1973			0.598026			0.299013	−	0.954249i	$-0.403343\pi$
$487$	13.1973			0.598026			0.299013	+	0.954249i	$0.403343\pi$
$488$	−5.56155	+	1.03399i	−0.251760	+	0.0468064i
$489$			9.12311i			0.412561i
$490$		0			0
$491$		−	31.5288i		−	1.42287i	−0.702750	−	0.711437i	$-0.748045\pi$
$491$		−	31.5288i		−	1.42287i	0.702750	−	0.711437i	$-0.251955\pi$
$492$	−2.64861	+	6.24621i	−0.119409	+	0.281601i
$493$	2.24621			0.101164
$494$	−11.1231	+	7.36520i	−0.500452	+	0.331376i
$495$		0			0
$496$	−9.43318	−	9.75379i	−0.423562	−	0.437958i
$497$	−16.0000	+	11.1231i	−0.717698	+	0.498939i
$498$	10.7575	−	7.12311i	0.482054	−	0.319194i
$499$			24.3266i			1.08901i	0.838758	+	0.544504i	$0.183282\pi$
$499$			24.3266i			1.08901i	−0.838758	+	0.544504i	$0.816718\pi$
$500$		0			0
$501$	−59.8617			−2.67443
$502$	−18.9309	+	12.5351i	−0.844926	+	0.559471i
$503$			17.9139i			0.798741i	0.916790	+	0.399370i	$0.130771\pi$
$503$			17.9139i			0.798741i	−0.916790	+	0.399370i	$0.869229\pi$
$504$	−32.2083	+	32.5915i	−1.43467	+	1.45174i
$505$		0			0
$506$	23.6155	+	35.6647i	1.04984	+	1.58549i
$507$			27.1840i			1.20729i
$508$	−13.8594	+	32.6847i	−0.614914	+	1.45015i
$509$			23.6155i			1.04674i	0.852106	+	0.523370i	$0.175325\pi$
$509$			23.6155i			1.04674i	−0.852106	+	0.523370i	$0.824675\pi$
$510$		0			0
$511$	23.2111	+	33.3880i	1.02680	+	1.47700i
$512$	−11.8551	−	19.2732i	−0.523927	−	0.851763i
$513$		−	44.4924i		−	1.96439i
$514$	13.4061	−	8.87689i	0.591318	−	0.391543i
$515$		0			0
$516$	−2.06798	−	0.876894i	−0.0910375	−	0.0386031i
$517$	−24.0000			−1.05552
$518$	2.76481	−	6.95383i	0.121479	−	0.305534i
$519$		−	49.0708i		−	2.15397i
$520$		0			0
$521$		−	9.75379i		−	0.427321i	−0.976908	−	0.213661i	$-0.931461\pi$
$521$		−	9.75379i		−	0.427321i	0.976908	−	0.213661i	$-0.0685387\pi$
$522$	14.4401	−	9.56155i	0.632025	−	0.418498i
$523$		−	19.2382i		−	0.841227i	−0.907240	−	0.420614i	$-0.861815\pi$
$523$		−	19.2382i		−	0.841227i	0.907240	−	0.420614i	$-0.138185\pi$
$524$	−13.6964	+	32.3002i	−0.598331	+	1.41104i
$525$		0			0
$526$	−21.8078	+	14.4401i	−0.950864	+	0.629618i
$527$	3.80989			0.165961
$528$	−39.6155	−	40.9620i	−1.72404	−	1.78264i
$529$	18.1231			0.787961
$530$		0			0
$531$	12.6624			0.549503
$532$	24.4279	−	5.11578i	1.05908	−	0.221797i
$533$			2.24621i			0.0972942i
$534$	42.7386	−	28.2995i	1.84948	−	1.22464i
$535$		0			0
$536$	−1.94602	−	10.4672i	−0.0840555	−	0.452113i
$537$	32.4924			1.40215
$538$	−0.192236	−	0.290319i	−0.00828788	−	0.0125166i
$539$	−30.9481	−	11.5012i	−1.33303	−	0.495390i
$540$		0			0
$541$	30.0000			1.28980			0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000			1.28980			0.644900	+	0.764267i	$0.276899\pi$
$542$	2.24621	−	1.48734i	0.0964830	−	0.0638866i
$543$	−45.6786			−1.96025
$544$	6.20393	+	1.36932i	0.265991	+	0.0587090i
$545$		0			0
$546$	−8.35097	+	21.0037i	−0.357388	+	0.898875i
$547$	30.5763			1.30735			0.653674	−	0.756776i	$-0.273227\pi$
$547$	30.5763			1.30735			0.653674	+	0.756776i	$0.273227\pi$
$548$	25.7782	+	10.9309i	1.10119	+	0.466944i
$549$		−	12.2462i		−	0.522656i
$550$		0			0
$551$	−9.43318			−0.401867
$552$	−53.8617	+	10.0138i	−2.29251	+	0.426216i
$553$	−2.87689	+	2.00000i	−0.122338	+	0.0850487i
$554$	9.56155	+	14.4401i	0.406231	+	0.613500i
$555$		0			0
$556$	13.1158	−	30.9309i	0.556233	−	1.31176i
$557$			26.4924i			1.12252i	0.827640	+	0.561260i	$0.189683\pi$
$557$			26.4924i			1.12252i	−0.827640	+	0.561260i	$0.810317\pi$
$558$	24.4924	−	16.2177i	1.03685	−	0.686552i
$559$	−0.743668			−0.0314538
$560$		0			0
$561$	16.0000			0.675521
$562$	34.6307	−	22.9309i	1.46081	−	0.967280i
$563$			38.1045i			1.60592i	0.596036	+	0.802958i	$0.296741\pi$
$563$			38.1045i			1.60592i	−0.596036	+	0.802958i	$0.703259\pi$
$564$	12.0000	−	28.2995i	0.505291	−	1.19163i
$565$		0			0
$566$	−3.84563	−	5.80776i	−0.161644	−	0.244119i
$567$	−15.2882	−	21.9912i	−0.642042	−	0.923544i
$568$	20.4810	−	3.80776i	0.859363	−	0.159770i
$569$	28.8769			1.21058			0.605291	−	0.796004i	$-0.293057\pi$
$569$	28.8769			1.21058			0.605291	+	0.796004i	$0.293057\pi$
$570$		0			0
$571$			3.22925i			0.135140i	0.997715	+	0.0675700i	$0.0215246\pi$
$571$			3.22925i			0.135140i	−0.997715	+	0.0675700i	$0.978475\pi$
$572$	−17.3693	−	7.36520i	−0.726248	−	0.307955i
$573$	50.7386			2.11964
$574$	1.55259	−	3.90495i	0.0648037	−	0.162989i
$575$		0			0
$576$	45.7116	−	17.6057i	1.90465	−	0.733571i
$577$	45.6155			1.89900			0.949500	−	0.313768i	$-0.101591\pi$
$577$	45.6155			1.89900			0.949500	+	0.313768i	$0.101591\pi$
$578$	18.5582	−	12.2884i	0.771918	−	0.511128i
$579$	−67.9372			−2.82337
$580$		0			0
$581$	−6.56155	+	4.56155i	−0.272219	+	0.189245i
$582$	−2.64861	−	4.00000i	−0.109789	−	0.165805i
$583$	−9.43318			−0.390682
$584$	−7.94584	−	42.7386i	−0.328801	−	1.76854i
$585$		0			0
$586$	−18.5760	+	12.3002i	−0.767369	+	0.508116i
$587$		−	21.8868i		−	0.903365i	−0.892179	−	0.451683i	$-0.850824\pi$
$587$		−	21.8868i		−	0.903365i	0.892179	−	0.451683i	$-0.149176\pi$
$588$	29.0356	−	30.7418i	1.19741	−	1.26777i
$589$	−16.0000			−0.659269
$590$		0			0
$591$	−54.3681			−2.23640
$592$	−5.75058	+	5.56155i	−0.236347	+	0.228578i
$593$	11.3693			0.466882			0.233441	−	0.972371i	$-0.425001\pi$
$593$	11.3693			0.466882			0.233441	+	0.972371i	$0.425001\pi$
$594$	52.4631	−	34.7386i	2.15259	−	1.42534i
$595$		0			0
$596$	−4.19224	+	9.88653i	−0.171721	+	0.404968i
$597$			80.9848i			3.31449i
$598$	−15.1231	+	10.0138i	−0.618430	+	0.409495i
$599$			29.6238i			1.21040i	0.796074	+	0.605199i	$0.206906\pi$
$599$			29.6238i			1.21040i	−0.796074	+	0.605199i	$0.793094\pi$
$600$		0			0
$601$			17.1231i			0.698466i	0.937036	+	0.349233i	$0.113558\pi$
$601$			17.1231i			0.698466i	−0.937036	+	0.349233i	$0.886442\pi$
$602$	1.29284	+	0.514026i	0.0526921	+	0.0209501i
$603$	23.0481			0.938590
$604$	−18.4384	−	7.81855i	−0.750250	−	0.318132i
$605$		0			0
$606$	53.8617	−	35.6647i	2.18798	−	1.44878i
$607$		−	37.9415i		−	1.54000i	−0.638045	−	0.769999i	$-0.720257\pi$
$607$		−	37.9415i		−	1.54000i	0.638045	−	0.769999i	$-0.279743\pi$
$608$	−26.0540	−	5.75058i	−1.05663	−	0.233217i
$609$	−13.1231	+	9.12311i	−0.531775	+	0.369687i
$610$		0			0
$611$		−	10.1768i		−	0.411711i
$612$	−5.36932	+	12.6624i	−0.217042	+	0.511848i
$613$			28.2462i			1.14085i	0.821348	+	0.570427i	$0.193222\pi$
$613$			28.2462i			1.14085i	−0.821348	+	0.570427i	$0.806778\pi$
$614$	−1.19702	−	1.80776i	−0.0483077	−	0.0729554i
$615$		0			0
$616$	25.1050	+	24.8098i	1.01151	+	0.999616i
$617$			26.0000i			1.04672i	0.852111	+	0.523360i	$0.175322\pi$
$617$			26.0000i			1.04672i	−0.852111	+	0.523360i	$0.824678\pi$
$618$	−27.5559	+	18.2462i	−1.10846	+	0.733970i
$619$	20.6083			0.828316			0.414158	−	0.910205i	$-0.364076\pi$
$619$	20.6083			0.828316			0.414158	+	0.910205i	$0.364076\pi$
$620$		0			0
$621$		−	60.4924i		−	2.42748i
$622$	35.6155	−	23.5829i	1.42805	−	0.945590i
$623$	−26.0685	+	18.1227i	−1.04441	+	0.726070i
$624$	17.3693	−	16.7984i	0.695329	−	0.672473i
$625$		0			0
$626$	39.6377	−	26.2462i	1.58424	−	1.04901i
$627$	−67.1935			−2.68345
$628$	−0.192236	+	0.453349i	−0.00767105	+	0.0180906i
$629$		−	2.24621i		−	0.0895623i
$630$		0			0
$631$		−	14.1498i		−	0.563293i	−0.959518	−	0.281647i	$-0.909119\pi$
$631$		−	14.1498i		−	0.563293i	0.959518	−	0.281647i	$-0.0908806\pi$
$632$	3.68260	−	0.684658i	0.146486	−	0.0272343i
$633$	66.7386			2.65262
$634$	9.56155	+	14.4401i	0.379738	+	0.573489i
$635$		0			0
$636$	4.71659	−	11.1231i	0.187025	−	0.441060i
$637$	4.87689	−	13.1231i	0.193230	−	0.519956i
$638$	−7.36520	−	11.1231i	−0.291591	−	0.440368i
$639$			45.0979i			1.78405i
$640$		0			0
$641$	−7.12311			−0.281346			−0.140673	−	0.990056i	$-0.544927\pi$
$641$	−7.12311			−0.281346			−0.140673	+	0.990056i	$0.544927\pi$
$642$	−13.3693	−	20.1907i	−0.527645	−	0.796862i
$643$		−	33.9686i		−	1.33959i	−0.742546	−	0.669795i	$-0.766382\pi$
$643$		−	33.9686i		−	1.33959i	0.742546	−	0.669795i	$-0.233618\pi$
$644$	33.2125	−	6.95547i	1.30875	−	0.274084i
$645$		0			0
$646$	6.24621	−	4.13595i	0.245754	−	0.162727i
$647$			40.1725i			1.57934i	0.613529	+	0.789672i	$0.289749\pi$
$647$			40.1725i			1.57934i	−0.613529	+	0.789672i	$0.710251\pi$
$648$	5.23358	+	28.1501i	0.205595	+	1.10584i
$649$		−	9.75379i		−	0.382870i
$650$		0			0
$651$	−22.2586	+	15.4741i	−0.872385	+	0.606477i
$652$	−2.35829	+	5.56155i	−0.0923579	+	0.217807i
$653$		−	22.9848i		−	0.899466i	−0.893163	−	0.449733i	$-0.851519\pi$
$653$		−	22.9848i		−	0.899466i	0.893163	−	0.449733i	$-0.148481\pi$
$654$	16.7984	+	25.3693i	0.656869	+	0.992019i
$655$		0			0
$656$	−3.22925	+	3.12311i	−0.126081	+	0.121937i
$657$	94.1080			3.67150
$658$	−7.03426	+	17.6920i	−0.274224	+	0.689707i
$659$		−	1.32431i		−	0.0515877i	−0.999667	−	0.0257938i	$-0.991789\pi$
$659$		−	1.32431i		−	0.0515877i	0.999667	−	0.0257938i	$-0.00821134\pi$
$660$		0			0
$661$		−	12.2462i		−	0.476322i	−0.971226	−	0.238161i	$-0.923455\pi$
$661$		−	12.2462i		−	0.476322i	0.971226	−	0.238161i	$-0.0765447\pi$
$662$	−14.2771	−	21.5616i	−0.554894	−	0.838014i
$663$			6.78456i			0.263491i
$664$	8.39919	−	1.56155i	0.325952	−	0.0606000i
$665$		0			0
$666$	−9.56155	−	14.4401i	−0.370503	−	0.559542i
$667$	−12.8255			−0.496604
$668$	−36.4924	−	15.4741i	−1.41193	−	0.598710i
$669$	−62.1080			−2.40123
$670$		0			0
$671$	−9.43318			−0.364164
$672$	−41.8069	+	17.1976i	−1.61274	+	0.663411i
$673$		−	14.0000i		−	0.539660i	−0.962908	−	0.269830i	$-0.913032\pi$
$673$		−	14.0000i		−	0.539660i	0.962908	−	0.269830i	$-0.0869676\pi$
$674$	−9.56155	−	14.4401i	−0.368297	−	0.556211i
$675$		0			0
$676$	−7.02699	+	16.5717i	−0.270269	+	0.637373i
$677$	−32.7386			−1.25825			−0.629124	−	0.777305i	$-0.716586\pi$
$677$	−32.7386			−1.25825			−0.629124	+	0.777305i	$0.716586\pi$
$678$	−65.8617	+	43.6106i	−2.52940	+	1.67485i
$679$	1.69614	+	2.43981i	0.0650919	+	0.0936313i
$680$		0			0
$681$	−11.3693			−0.435673
$682$	−12.4924	−	18.8664i	−0.478360	−	0.722430i
$683$	0.371834			0.0142278			0.00711392	−	0.999975i	$-0.497736\pi$
$683$	0.371834			0.0142278			0.00711392	+	0.999975i	$0.497736\pi$
$684$	22.5490	−	53.1771i	0.862181	−	2.03328i
$685$		0			0
$686$	−17.5490	+	19.4431i	−0.670024	+	0.742339i
$687$	38.8940			1.48390
$688$	−1.03399	−	1.06913i	−0.0394204	−	0.0407602i
$689$		−	4.00000i		−	0.152388i
$690$		0			0
$691$	14.8934			0.566573			0.283286	−	0.959035i	$-0.408575\pi$
$691$	14.8934			0.566573			0.283286	+	0.959035i	$0.408575\pi$
$692$	12.6847	−	29.9142i	0.482198	−	1.13717i
$693$	−62.7386	+	43.6155i	−2.38324	+	1.65682i
$694$	6.68466	−	4.42627i	0.253746	−	0.168019i
$695$		0			0
$696$	16.7984	−	3.12311i	0.636741	−	0.118381i
$697$		−	1.26137i		−	0.0477777i
$698$	23.3153	+	35.2114i	0.882499	+	1.33277i
$699$	23.4199			0.885823
$700$		0			0
$701$	11.1231			0.420114			0.210057	−	0.977689i	$-0.432635\pi$
$701$	11.1231			0.420114			0.210057	+	0.977689i	$0.432635\pi$
$702$	14.7304	+	22.2462i	0.555963	+	0.839629i
$703$			9.43318i			0.355779i
$704$	−13.5616	−	35.2114i	−0.511120	−	1.32708i
$705$		0			0
$706$	−22.8393	+	15.1231i	−0.859568	+	0.569166i
$707$	−32.8531	+	22.8393i	−1.23557	+	0.858959i
$708$	11.5012	+	4.87689i	0.432240	+	0.183285i
$709$	−44.7386			−1.68019			−0.840097	−	0.542436i	$-0.817502\pi$
$709$	−44.7386			−1.68019			−0.840097	+	0.542436i	$0.817502\pi$
$710$		0			0
$711$			8.10887i			0.304106i
$712$	33.3693	−	6.20393i	1.25057	−	0.232502i
$713$	−21.7538			−0.814686
$714$	4.68951	−	11.7947i	0.175500	−	0.441405i
$715$		0			0
$716$	19.8078	+	8.39919i	0.740251	+	0.313892i
$717$	−12.0000			−0.448148
$718$	12.5351	+	18.9309i	0.467807	+	0.706494i
$719$	22.6762			0.845681			0.422841	−	0.906204i	$-0.361033\pi$
$719$	22.6762			0.845681			0.422841	+	0.906204i	$0.361033\pi$
$720$		0			0
$721$	16.8078	−	11.6847i	0.625954	−	0.435159i
$722$	−3.82776	+	2.53457i	−0.142455	+	0.0943267i
$723$	−77.3704			−2.87743
$724$	−27.8462	−	11.8078i	−1.03490	−	0.438832i
$725$		0			0
$726$	−26.5219	−	40.0540i	−0.984319	−	1.48654i
$727$		−	9.64198i		−	0.357601i	−0.983885	−	0.178801i	$-0.942778\pi$
$727$		−	9.64198i		−	0.357601i	0.983885	−	0.178801i	$-0.0572217\pi$
$728$	−10.5202	+	10.6454i	−0.389906	+	0.394545i
$729$	23.4924			0.870090
$730$		0			0
$731$	0.417609			0.0154458
$732$	4.71659	−	11.1231i	0.174330	−	0.411122i
$733$	−0.738634			−0.0272821			−0.0136410	−	0.999907i	$-0.504342\pi$
$733$	−0.738634			−0.0272821			−0.0136410	+	0.999907i	$0.504342\pi$
$734$	8.10887	+	12.2462i	0.299304	+	0.452016i
$735$		0			0
$736$	−35.4233	−	7.81855i	−1.30572	−	0.288196i
$737$		−	17.7538i		−	0.653969i
$738$	−5.36932	−	8.10887i	−0.197647	−	0.298492i
$739$		−	37.5697i		−	1.38202i	−0.722844	−	0.691012i	$-0.757165\pi$
$739$		−	37.5697i		−	1.38202i	0.722844	−	0.691012i	$-0.242835\pi$
$740$		0			0
$741$		−	28.4924i		−	1.04670i
$742$	−2.76481	+	6.95383i	−0.101499	+	0.255283i
$743$	−23.7917			−0.872835			−0.436417	−	0.899744i	$-0.643753\pi$
$743$	−23.7917			−0.872835			−0.436417	+	0.899744i	$0.643753\pi$
$744$	28.4924	−	5.29723i	1.04458	−	0.194206i
$745$		0			0
$746$	8.19224	+	12.3721i	0.299939	+	0.452975i
$747$			18.4945i			0.676679i
$748$	9.75379	+	4.13595i	0.356634	+	0.151225i
$749$	8.56155	+	12.3153i	0.312832	+	0.449993i
$750$		0			0
$751$		−	28.8802i		−	1.05385i	−0.849911	−	0.526926i	$-0.823344\pi$
$751$		−	28.8802i		−	1.05385i	0.849911	−	0.526926i	$-0.176656\pi$
$752$	14.6307	−	14.1498i	0.533526	−	0.515989i
$753$		−	48.4924i		−	1.76716i
$754$	4.71659	−	3.12311i	0.171768	−	0.113737i
$755$		0			0
$756$	−10.2316	−	48.8558i	−0.372118	−	1.77687i
$757$		−	4.24621i		−	0.154331i	−0.997018	−	0.0771656i	$-0.975413\pi$
$757$		−	4.24621i		−	0.154331i	0.997018	−	0.0771656i	$-0.0245870\pi$
$758$	11.6284	+	17.5616i	0.422364	+	0.637864i
$759$	−91.3571			−3.31605
$760$		0			0
$761$		−	47.2311i		−	1.71212i	−0.516873	−	0.856062i	$-0.672904\pi$
$761$		−	47.2311i		−	1.71212i	0.516873	−	0.856062i	$-0.327096\pi$
$762$	−41.8617	−	63.2206i	−1.51649	−	2.29024i
$763$	−10.7575	−	15.4741i	−0.389447	−	0.560199i
$764$	30.9309	+	13.1158i	1.11904	+	0.474512i
$765$		0			0
$766$	−14.8934	−	22.4924i	−0.538122	−	0.812684i
$767$	4.13595			0.149341
$768$	48.3002	+	1.61463i	1.74288	+	0.0582628i
$769$			27.2311i			0.981977i	0.871166	+	0.490989i	$0.163364\pi$
$769$			27.2311i			0.981977i	−0.871166	+	0.490989i	$0.836636\pi$
$770$		0			0
$771$			34.3404i			1.23674i
$772$	−41.4153	−	17.5616i	−1.49057	−	0.632054i
$773$	32.7386			1.17753			0.588763	−	0.808305i	$-0.299615\pi$
$773$	32.7386			1.17753			0.588763	+	0.808305i	$0.299615\pi$
$774$	2.68466	−	1.77766i	0.0964981	−	0.0638965i
$775$		0			0
$776$	−0.580639	−	3.12311i	−0.0208437	−	0.112113i
$777$	9.12311	+	13.1231i	0.327290	+	0.470789i
$778$	−8.39919	+	5.56155i	−0.301126	+	0.199391i
$779$			5.29723i			0.189793i
$780$		0			0
$781$	34.7386			1.24305
$782$	8.49242	−	5.62329i	0.303688	−	0.201088i
$783$			18.8664i			0.674229i
$784$	25.6471	−	11.2350i	0.915969	−	0.401249i
$785$		0			0
$786$	−41.3693	−	62.4769i	−1.47559	−	2.22848i
$787$			3.02045i			0.107667i	0.998550	+	0.0538337i	$0.0171441\pi$
$787$			3.02045i			0.107667i	−0.998550	+	0.0538337i	$0.982856\pi$
$788$	−33.1434	−	14.0540i	−1.18069	−	0.500652i
$789$		−	55.8617i		−	1.98873i
$790$		0			0
$791$	40.1725	−	27.9277i	1.42837	−	0.992995i
$792$	80.3093	−	14.9309i	2.85367	−	0.530545i
$793$		−	4.00000i		−	0.142044i
$794$	16.5081	−	10.9309i	0.585849	−	0.387922i
$795$		0			0
$796$	−20.9343	+	49.3693i	−0.741998	+	1.74985i
$797$	−3.75379			−0.132966			−0.0664830	−	0.997788i	$-0.521178\pi$
$797$	−3.75379			−0.132966			−0.0664830	+	0.997788i	$0.521178\pi$
$798$	−19.6940	+	49.5329i	−0.697162	+	1.75345i
$799$			5.71484i			0.202176i
$800$		0			0
$801$			73.4773i			2.59619i
$802$	−7.07488	+	4.68466i	−0.249823	+	0.165421i
$803$		−	72.4908i		−	2.55814i
$804$	20.9343	+	8.87689i	0.738297	+	0.313064i
$805$		0			0
$806$	8.00000	−	5.29723i	0.281788	−	0.186587i
$807$	0.743668			0.0261784
$808$	42.0540	−	7.81855i	1.47945	−	0.275056i
$809$	−46.9848			−1.65190			−0.825950	−	0.563744i	$-0.809360\pi$
$809$	−46.9848			−1.65190			−0.825950	+	0.563744i	$0.809360\pi$
$810$		0			0
$811$	−8.10887			−0.284741			−0.142370	−	0.989813i	$-0.545472\pi$
$811$	−8.10887			−0.284741			−0.142370	+	0.989813i	$0.545472\pi$
$812$	−10.3583	+	2.16927i	−0.363505	+	0.0761265i
$813$			5.75379i			0.201794i
$814$	−11.1231	+	7.36520i	−0.389865	+	0.258150i
$815$		0			0
$816$	−9.75379	+	9.43318i	−0.341451	+	0.330227i
$817$	−1.75379			−0.0613573
$818$	−13.3693	−	20.1907i	−0.467447	−	0.705950i
$819$	−18.4945	−	26.6034i	−0.646251	−	0.929598i
$820$		0			0
$821$	15.6155			0.544986			0.272493	−	0.962158i	$-0.412152\pi$
$821$	15.6155			0.544986			0.272493	+	0.962158i	$0.412152\pi$
$822$	−49.8617	+	33.0161i	−1.73913	+	1.15157i
$823$	29.0890			1.01398			0.506989	−	0.861953i	$-0.330758\pi$
$823$	29.0890			1.01398			0.506989	+	0.861953i	$0.330758\pi$
$824$	−21.5150	+	4.00000i	−0.749509	+	0.139347i
$825$		0			0
$826$	−7.19018	−	2.85878i	−0.250178	−	0.0994697i
$827$	−24.5354			−0.853180			−0.426590	−	0.904445i	$-0.640285\pi$
$827$	−24.5354			−0.853180			−0.426590	+	0.904445i	$0.640285\pi$
$828$	30.6578	−	72.3002i	1.06543	−	2.51261i
$829$		−	15.7538i		−	0.547152i	−0.961850	−	0.273576i	$-0.911794\pi$
$829$		−	15.7538i		−	0.547152i	0.961850	−	0.273576i	$-0.0882065\pi$
$830$		0			0
$831$	−36.9890			−1.28314
$832$	14.9309	−	5.75058i	0.517635	−	0.199365i
$833$	−2.73863	+	7.36932i	−0.0948880	+	0.255332i
$834$	39.6155	+	59.8283i	1.37177	+	2.07169i
$835$		0			0
$836$	−40.9620	−	17.3693i	−1.41670	−	0.600730i
$837$			32.0000i			1.10608i
$838$	27.8078	−	18.4130i	0.960603	−	0.636067i
$839$	10.9205			0.377018			0.188509	−	0.982071i	$-0.439635\pi$
$839$	10.9205			0.377018			0.188509	+	0.982071i	$0.439635\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−27.8462	+	18.4384i	−0.959643	+	0.635431i
$843$			88.7085i			3.05528i
$844$	40.6847	+	17.2517i	1.40042	+	0.593829i
$845$		0			0
$846$	24.3266	+	36.7386i	0.836366	+	1.26310i
$847$	16.9843	+	24.4310i	0.583587	+	0.839460i
$848$	5.75058	−	5.56155i	0.197476	−	0.190985i
$849$	14.8769			0.510574
$850$		0			0
$851$			12.8255i			0.439651i
$852$	−17.3693	+	40.9620i	−0.595063	+	1.40333i
$853$	−24.2462			−0.830174			−0.415087	−	0.909782i	$-0.636249\pi$
$853$	−24.2462			−0.830174			−0.415087	+	0.909782i	$0.636249\pi$
$854$	−2.76481	+	6.95383i	−0.0946099	+	0.237955i
$855$		0			0
$856$	−2.93087	−	15.7644i	−0.100175	−	0.538816i
$857$	25.6155			0.875010			0.437505	−	0.899216i	$-0.355862\pi$
$857$	25.6155			0.875010			0.437505	+	0.899216i	$0.355862\pi$
$858$	33.5968	−	22.2462i	1.14697	−	0.759473i
$859$	−3.55531			−0.121306			−0.0606528	−	0.998159i	$-0.519318\pi$
$859$	−3.55531			−0.121306			−0.0606528	+	0.998159i	$0.519318\pi$
$860$		0			0
$861$	5.12311	+	7.36932i	0.174595	+	0.251146i
$862$	−4.58930	−	6.93087i	−0.156312	−	0.236066i
$863$	10.2226			0.347982			0.173991	−	0.984747i	$-0.444334\pi$
$863$	10.2226			0.347982			0.173991	+	0.984747i	$0.444334\pi$
$864$	−11.5012	+	52.1080i	−0.391277	+	1.77275i
$865$		0			0
$866$	34.9211	−	23.1231i	1.18667	−	0.785755i
$867$			47.5377i			1.61447i
$868$	−17.5691	+	3.67939i	−0.596335	+	0.124887i
$869$	6.24621			0.211888
$870$		0			0
$871$	7.52823			0.255084
$872$	3.68260	+	19.8078i	0.124709	+	0.670776i
$873$	6.87689			0.232748
$874$	−35.6647	+	23.6155i	−1.20638	+	0.798807i
$875$		0			0
$876$	85.4773	+	36.2454i	2.88801	+	1.22462i
$877$		−	0.738634i		−	0.0249419i	−0.999922	−	0.0124709i	$-0.996030\pi$
$877$		−	0.738634i		−	0.0249419i	0.999922	−	0.0124709i	$-0.00396973\pi$
$878$	−19.1231	+	12.6624i	−0.645374	+	0.427336i
$879$		−	47.5835i		−	1.60495i
$880$		0			0
$881$			31.3693i			1.05686i	0.848977	+	0.528430i	$0.177219\pi$
$881$			31.3693i			1.05686i	−0.848977	+	0.528430i	$0.822781\pi$
$882$	13.7636	+	59.0324i	0.463445	+	1.98772i
$883$	31.3200			1.05400			0.527001	−	0.849865i	$-0.323317\pi$
$883$	31.3200			1.05400			0.527001	+	0.849865i	$0.323317\pi$
$884$	−1.75379	+	4.13595i	−0.0589863	+	0.139107i
$885$		0			0
$886$	−27.1771	+	17.9954i	−0.913032	+	0.604567i
$887$			29.9957i			1.00716i	0.863950	+	0.503578i	$0.167983\pi$
$887$			29.9957i			1.00716i	−0.863950	+	0.503578i	$0.832017\pi$
$888$	−3.12311	−	16.7984i	−0.104805	−	0.563717i
$889$	26.8078	+	38.5616i	0.899104	+	1.29331i
$890$		0			0
$891$			47.7465i			1.59957i
$892$	−37.8617	−	16.0547i	−1.26770	−	0.537552i
$893$		−	24.0000i		−	0.803129i
$894$	−12.6624	−	19.1231i	−0.423495	−	0.639572i
$895$		0			0
$896$	−29.9315	−	0.323119i	−0.999942	−	0.0107946i
$897$		−	38.7386i		−	1.29345i
$898$	−18.4130	+	12.1922i	−0.614450	+	0.406860i
$899$	6.78456			0.226278
$900$		0			0
$901$			2.24621i			0.0748321i
$902$	−6.24621	+	4.13595i	−0.207976	+	0.137712i
$903$	−2.43981	+	1.69614i	−0.0811918	+	0.0564440i
$904$	−51.4233	+	9.56047i	−1.71031	+	0.317976i
$905$		0			0
$906$	35.6647	−	23.6155i	1.18488	−	0.784573i
$907$	52.8350			1.75436			0.877178	−	0.480166i	$-0.159423\pi$
$907$	52.8350			1.75436			0.877178	+	0.480166i	$0.159423\pi$
$908$	−6.93087	−	2.93893i	−0.230009	−	0.0975319i
$909$			92.6004i			3.07136i
$910$		0			0
$911$			2.06798i			0.0685151i	0.999413	+	0.0342575i	$0.0109066\pi$
$911$			2.06798i			0.0685151i	−0.999413	+	0.0342575i	$0.989093\pi$
$912$	40.9620	−	39.6155i	1.35639	−	1.31180i
$913$	14.2462			0.471481
$914$	4.68466	+	7.07488i	0.154955	+	0.234016i
$915$		0			0
$916$	23.7102	+	10.0540i	0.783408	+	0.332193i
$917$	26.4924	+	38.1080i	0.874857	+	1.25844i
$918$	−8.27190	−	12.4924i	−0.273013	−	0.412311i
$919$			9.27015i			0.305794i	0.988242	+	0.152897i	$0.0488603\pi$
$919$			9.27015i			0.305794i	−0.988242	+	0.152897i	$0.951140\pi$
$920$		0			0
$921$	4.63068			0.152586
$922$	−2.82292	−	4.26324i	−0.0929679	−	0.140402i
$923$			14.7304i			0.484857i
$924$	−73.7832	+	15.4519i	−2.42729	+	0.508332i
$925$		0			0
$926$	−33.8078	+	22.3859i	−1.11099	+	0.735647i
$927$		−	47.3747i		−	1.55599i
$928$	11.0478	+	2.43845i	0.362662	+	0.0800460i
$929$			21.1231i			0.693027i	0.938045	+	0.346513i	$0.112634\pi$
$929$			21.1231i			0.693027i	−0.938045	+	0.346513i	$0.887366\pi$
$930$		0			0
$931$	11.5012	−	30.9481i	0.376935	−	1.01428i
$932$	14.2771	+	6.05398i	0.467661	+	0.198305i
$933$			91.2311i			2.98677i
$934$	−14.4401	−	21.8078i	−0.472494	−	0.713572i
$935$		0			0
$936$	6.33122	+	34.0540i	0.206942	+	1.11309i
$937$	−38.1080			−1.24493			−0.622466	−	0.782647i	$-0.713869\pi$
$937$	−38.1080			−1.24493			−0.622466	+	0.782647i	$0.713869\pi$
$938$	−13.0875	−	5.20354i	−0.427323	−	0.169901i
$939$			101.534i			3.31344i
$940$		0			0
$941$			26.6307i			0.868135i	0.900880	+	0.434068i	$0.142922\pi$
$941$			26.6307i			0.868135i	−0.900880	+	0.434068i	$0.857078\pi$
$942$	−0.580639	−	0.876894i	−0.0189182	−	0.0285708i
$943$			7.20217i			0.234535i
$944$	5.75058	+	5.94602i	0.187165	+	0.193527i
$945$		0			0
$946$	−1.36932	−	2.06798i	−0.0445203	−	0.0672357i
$947$	35.8735			1.16573			0.582867	−	0.812568i	$-0.301931\pi$
$947$	35.8735			1.16573			0.582867	+	0.812568i	$0.301931\pi$
$948$	−3.12311	+	7.36520i	−0.101434	+	0.239211i
$949$	30.7386			0.997818
$950$		0			0
$951$	−36.9890			−1.19945
$952$	5.90767	−	5.97796i	0.191469	−	0.193747i
$953$			28.2462i			0.914985i	0.889214	+	0.457492i	$0.151252\pi$
$953$			28.2462i			0.914985i	−0.889214	+	0.457492i	$0.848748\pi$
$954$	9.56155	+	14.4401i	0.309567	+	0.467515i
$955$		0			0
$956$	−7.31534	−	3.10196i	−0.236595	−	0.100325i
$957$	28.4924			0.921029
$958$		0			0
$959$	30.4133	−	21.1431i	0.982096	−	0.682747i
$960$		0			0
$961$	−19.4924			−0.628788
$962$	−3.12311	−	4.71659i	−0.100693	−	0.152069i
$963$	34.7123			1.11859
$964$	−47.1659	−	20.0000i	−1.51911	−	0.644157i
$965$		0			0
$966$	−26.7763	+	67.3455i	−0.861512	+	2.16681i
$967$	3.43806			0.110560			0.0552802	−	0.998471i	$-0.482395\pi$
$967$	3.43806			0.110560			0.0552802	+	0.998471i	$0.482395\pi$
$968$	−5.81422	−	31.2732i	−0.186876	−	1.00516i
$969$			16.0000i			0.513994i
$970$		0			0
$971$	10.7575			0.345224			0.172612	−	0.984990i	$-0.444779\pi$
$971$	10.7575			0.345224			0.172612	+	0.984990i	$0.444779\pi$
$972$	−4.19224	−	1.77766i	−0.134466	−	0.0570183i
$973$	−25.3693	−	36.4924i	−0.813303	−	1.16989i
$974$	−15.5616	+	10.3041i	−0.498624	+	0.330166i
$975$		0			0
$976$	5.75058	−	5.56155i	0.184071	−	0.178021i
$977$		−	22.4924i		−	0.719596i	−0.933030	−	0.359798i	$-0.882846\pi$
$977$		−	22.4924i		−	0.719596i	0.933030	−	0.359798i	$-0.117154\pi$
$978$	−7.12311	−	10.7575i	−0.227772	−	0.343986i
$979$	56.5991			1.80891
$980$		0			0
$981$	−43.6155			−1.39254
$982$	24.6169	+	37.1771i	0.785558	+	1.18637i
$983$		−	28.5083i		−	0.909275i	−0.890677	−	0.454637i	$-0.849769\pi$
$983$		−	28.5083i		−	0.909275i	0.890677	−	0.454637i	$-0.150231\pi$
$984$	−1.75379	−	9.43318i	−0.0559087	−	0.300719i
$985$		0			0
$986$	−2.64861	+	1.75379i	−0.0843490	+	0.0558520i
$987$	−23.2111	−	33.3880i	−0.738818	−	1.06275i
$988$	7.36520	−	17.3693i	0.234318	−	0.552592i
$989$	−2.38447			−0.0758218
$990$		0			0
$991$		−	48.9078i		−	1.55361i	−0.629743	−	0.776804i	$-0.716840\pi$
$991$		−	48.9078i		−	1.55361i	0.629743	−	0.776804i	$-0.283160\pi$
$992$	18.7386	+	4.13595i	0.594952	+	0.131317i
$993$	55.2311			1.75270
$994$	10.1817	−	25.6082i	0.322944	−	0.812243i
$995$		0			0
$996$	−7.12311	+	16.7984i	−0.225704	+	0.532277i
$997$	−5.50758			−0.174427			−0.0872134	−	0.996190i	$-0.527796\pi$
$997$	−5.50758			−0.174427			−0.0872134	+	0.996190i	$0.527796\pi$
$998$	−18.9936	−	28.6847i	−0.601233	−	0.907997i
$999$	18.8664			0.596905

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.c.i.699.2		8
4.3	odd	2	inner	700.2.c.i.699.8		8
5.2	odd	4		140.2.g.c.111.1	✓	8
5.3	odd	4		700.2.g.j.251.8		8
5.4	even	2		700.2.c.j.699.7		8
7.6	odd	2		700.2.c.j.699.2		8
15.2	even	4		1260.2.c.c.811.7		8
20.3	even	4		700.2.g.j.251.5		8
20.7	even	4		140.2.g.c.111.4	yes	8
20.19	odd	2		700.2.c.j.699.1		8
28.27	even	2		700.2.c.j.699.8		8
35.2	odd	12		980.2.o.e.31.4		16
35.12	even	12		980.2.o.e.31.3		16
35.13	even	4		700.2.g.j.251.7		8
35.17	even	12		980.2.o.e.411.7		16
35.27	even	4		140.2.g.c.111.2	yes	8
35.32	odd	12		980.2.o.e.411.8		16
35.34	odd	2	inner	700.2.c.i.699.7		8
40.27	even	4		2240.2.k.e.1791.1		8
40.37	odd	4		2240.2.k.e.1791.7		8
60.47	odd	4		1260.2.c.c.811.5		8
105.62	odd	4		1260.2.c.c.811.8		8
140.27	odd	4		140.2.g.c.111.3	yes	8
140.47	odd	12		980.2.o.e.31.8		16
140.67	even	12		980.2.o.e.411.3		16
140.83	odd	4		700.2.g.j.251.6		8
140.87	odd	12		980.2.o.e.411.4		16
140.107	even	12		980.2.o.e.31.7		16
140.139	even	2	inner	700.2.c.i.699.1		8
280.27	odd	4		2240.2.k.e.1791.8		8
280.237	even	4		2240.2.k.e.1791.2		8
420.167	even	4		1260.2.c.c.811.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.g.c.111.1	✓	8	5.2	odd	4
140.2.g.c.111.2	yes	8	35.27	even	4
140.2.g.c.111.3	yes	8	140.27	odd	4
140.2.g.c.111.4	yes	8	20.7	even	4
700.2.c.i.699.1		8	140.139	even	2	inner
700.2.c.i.699.2		8	1.1	even	1	trivial
700.2.c.i.699.7		8	35.34	odd	2	inner
700.2.c.i.699.8		8	4.3	odd	2	inner
700.2.c.j.699.1		8	20.19	odd	2
700.2.c.j.699.2		8	7.6	odd	2
700.2.c.j.699.7		8	5.4	even	2
700.2.c.j.699.8		8	28.27	even	2
700.2.g.j.251.5		8	20.3	even	4
700.2.g.j.251.6		8	140.83	odd	4
700.2.g.j.251.7		8	35.13	even	4
700.2.g.j.251.8		8	5.3	odd	4
980.2.o.e.31.3		16	35.12	even	12
980.2.o.e.31.4		16	35.2	odd	12
980.2.o.e.31.7		16	140.107	even	12
980.2.o.e.31.8		16	140.47	odd	12
980.2.o.e.411.3		16	140.67	even	12
980.2.o.e.411.4		16	140.87	odd	12
980.2.o.e.411.7		16	35.17	even	12
980.2.o.e.411.8		16	35.32	odd	12
1260.2.c.c.811.5		8	60.47	odd	4
1260.2.c.c.811.6		8	420.167	even	4
1260.2.c.c.811.7		8	15.2	even	4
1260.2.c.c.811.8		8	105.62	odd	4
2240.2.k.e.1791.1		8	40.27	even	4
2240.2.k.e.1791.2		8	280.237	even	4
2240.2.k.e.1791.7		8	40.37	odd	4
2240.2.k.e.1791.8		8	280.27	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.17915 + 0.780776i) q^{2} -3.02045i q^{3} +(0.780776 - 1.84130i) q^{4} +(2.35829 + 3.56155i) q^{6} +(-1.51022 - 2.17238i) q^{7} +(0.516994 + 2.78078i) q^{8} -6.12311 q^{9} +O(q^{10})\)	\(q+(-1.17915 + 0.780776i) q^{2} -3.02045i q^{3} +(0.780776 - 1.84130i) q^{4} +(2.35829 + 3.56155i) q^{6} +(-1.51022 - 2.17238i) q^{7} +(0.516994 + 2.78078i) q^{8} -6.12311 q^{9} +4.71659i q^{11} +(-5.56155 - 2.35829i) q^{12} -2.00000 q^{13} +(3.47692 + 1.38241i) q^{14} +(-2.78078 - 2.87529i) q^{16} +1.12311 q^{17} +(7.22004 - 4.78078i) q^{18} -4.71659 q^{19} +(-6.56155 + 4.56155i) q^{21} +(-3.68260 - 5.56155i) q^{22} -6.41273 q^{23} +(8.39919 - 1.56155i) q^{24} +(2.35829 - 1.56155i) q^{26} +9.43318i q^{27} +(-5.17915 + 1.08464i) q^{28} +2.00000 q^{29} +3.39228 q^{31} +(5.52390 + 1.21922i) q^{32} +14.2462 q^{33} +(-1.32431 + 0.876894i) q^{34} +(-4.78078 + 11.2745i) q^{36} -2.00000i q^{37} +(5.56155 - 3.68260i) q^{38} +6.04090i q^{39} -1.12311i q^{41} +(4.17548 - 10.5018i) q^{42} +0.371834 q^{43} +(8.68466 + 3.68260i) q^{44} +(7.56155 - 5.00691i) q^{46} +5.08842i q^{47} +(-8.68466 + 8.39919i) q^{48} +(-2.43845 + 6.56155i) q^{49} -3.39228i q^{51} +(-1.56155 + 3.68260i) q^{52} +2.00000i q^{53} +(-7.36520 - 11.1231i) q^{54} +(5.26012 - 5.32270i) q^{56} +14.2462i q^{57} +(-2.35829 + 1.56155i) q^{58} -2.06798 q^{59} +2.00000i q^{61} +(-4.00000 + 2.64861i) q^{62} +(9.24726 + 13.3017i) q^{63} +(-7.46543 + 2.87529i) q^{64} +(-16.7984 + 11.1231i) q^{66} -3.76412 q^{67} +(0.876894 - 2.06798i) q^{68} +19.3693i q^{69} -7.36520i q^{71} +(-3.16561 - 17.0270i) q^{72} -15.3693 q^{73} +(1.56155 + 2.35829i) q^{74} +(-3.68260 + 8.68466i) q^{76} +(10.2462 - 7.12311i) q^{77} +(-4.71659 - 7.12311i) q^{78} -1.32431i q^{79} +10.1231 q^{81} +(0.876894 + 1.32431i) q^{82} -3.02045i q^{83} +(3.27608 + 15.6433i) q^{84} +(-0.438447 + 0.290319i) q^{86} -6.04090i q^{87} +(-13.1158 + 2.43845i) q^{88} -12.0000i q^{89} +(3.02045 + 4.34475i) q^{91} +(-5.00691 + 11.8078i) q^{92} -10.2462i q^{93} +(-3.97292 - 6.00000i) q^{94} +(3.68260 - 16.6847i) q^{96} -1.12311 q^{97} +(-2.24782 - 9.64092i) q^{98} -28.8802i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 16 q^{9}+O(q^{10}) \) 8 * q - 2 * q^4 - 16 * q^9	\( 8 q - 2 q^{4} - 16 q^{9} - 28 q^{12} - 16 q^{13} + 6 q^{14} - 14 q^{16} - 24 q^{17} - 36 q^{21} - 32 q^{28} + 16 q^{29} + 48 q^{33} - 30 q^{36} + 28 q^{38} - 12 q^{42} + 20 q^{44} + 44 q^{46} - 20 q^{48} - 36 q^{49} + 4 q^{52} + 2 q^{56} - 32 q^{62} - 2 q^{64} + 40 q^{68} - 24 q^{73} - 4 q^{74} + 16 q^{77} + 48 q^{81} + 40 q^{82} - 8 q^{84} - 20 q^{86} + 24 q^{97} - 8 q^{98}+O(q^{100}) \) 8 * q - 2 * q^4 - 16 * q^9 - 28 * q^12 - 16 * q^13 + 6 * q^14 - 14 * q^16 - 24 * q^17 - 36 * q^21 - 32 * q^28 + 16 * q^29 + 48 * q^33 - 30 * q^36 + 28 * q^38 - 12 * q^42 + 20 * q^44 + 44 * q^46 - 20 * q^48 - 36 * q^49 + 4 * q^52 + 2 * q^56 - 32 * q^62 - 2 * q^64 + 40 * q^68 - 24 * q^73 - 4 * q^74 + 16 * q^77 + 48 * q^81 + 40 * q^82 - 8 * q^84 - 20 * q^86 + 24 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more